(a) The earth- moon distance is about 60 earth radius. What wil be the diameter of the earth (approximately in degress) as seen from the moon ? (b) Moon is seen to be of `(1//2)^@` diameter from the earth. What must be the relative size compared to the earth ? (c ) From parallax measurement, the sun is found to be at a distance of about 400 times the earth. moon distance. Estimate the ratio of sun-earth diameters.

Explanation

(a) Considering the given data, we have
`theta= ("Diameter of earth",D_("earth"))/("Distance between earth and moon,"r_("moon"))`
`=(2R_("earth"))/(60R_("earth"))=1.9^(@)=2^(@)`
Thus, the diameter of the earth as seen from the moon is `2^(@)`.

(b) Now, for moon, we have

Now, `theta= (D_("moon"))/(r_("moon"))= (2R_("moon"))/(60R_("earth"))= (R_("moon"))/(30R_("earth"))`
`=(1)/(2)xx(pi)/(180)"rad"= (pi)/(360)"rad"`
`=(D_("moon"))/(D_("earth"))=(R_("moon"))/(R_("earth"))= (30pi)/(360)=(pi)/(12)=0.26 = (1)/(4)`
or `(D_("earth"))/(D_("moon"))=4" "".........."(ii)`
So, the earth is approximately four times the moon.
(c ) `(r_("sun"))/(r_("moon"))= ("Distance of sun from earth")/("Distance of moon from earth")= 400" ""..........."(iii)`
The sun and the moon both appear to be of the same angular diameter as seen from the earth.
`theta= (D_("sun"))/(r_("sun"))= (D_("moon"))/(r_("moon"))`
or `(D_("sun"))/(D_("moon"))= (r_("sun"))/(r_("moon"))=400" "".........."(iv)`
But from equation, (ii), we have
`(D_("earth"))/(D_("moon"))=4" ""............"(v)`
`(D_("sun"))/(D_("earth"))=(400)/(4)=100`.